Coulomb disorder in three-dimensional Dirac systems

Abstract

In three-dimensional materials with a Dirac spectrum, weak short-ranged disorder is essentially irrelevant near the Dirac point. This is manifestly not the case for Coulomb disorder, where the long-ranged nature of the potential produced by charged impurities implies large fluctuations of the disorder potential even when impurities are sparse, and these fluctuations are screened by the formation of electron/hole puddles. In this paper I present a theory of such nonlinear screening of Coulomb disorder in three-dimensional Dirac systems, and I derive the typical magnitude of the disorder potential, the corresponding density of states, and the size and density of electron/hole puddles. The resulting conductivity is also discussed.

5 pages, 2 figures

References in corpus (6)

• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Rare region effects dominate weakly disordered 3D Dirac points
• Why is the bulk resistivity of topological insulators so small?
• Statistics of random voltage fluctuations and the low-density residual conductivity of graphene
• Theory of the random potential and conductivity at the surface of a topological insulator
• A simple model of Coulomb disorder and screening in graphene

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• Quantum transport in three-dimensional Weyl electron system -- in the presence of charged impurity scattering
• Charge transport in gapless chiral electron systems with arbitrary band dispersion